{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -48*(2*X+1)^2*(18*X^2+18*X+13), 746496*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\kappa$", "degz": 2, "h3": null, "sol": "1 624 685584 883925760 1229988226320 1789812200058624 2682147441688678656 4103873321005267070976 6377307485242500121320720 10029763457800404355003549440", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -624 -3360 -6816 -6912 -3456 2239488 10450944 17169408 11943936 2985984", "new_number": "2.59", "id": 54, "operator_tex": "\\theta^4-2^{4} 3 x(2\\theta+1)^2(18\\theta^2+18\\theta+13)+2^{10} 3^{6} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "-384 -164736", "discriminant": "2 1 -3456 2985984", "aesz": "47", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "792da990d2d2e5263bb789ad37b00d44", "dim_h": null, "inst": " -384 -1356 -164736 96211836 -3267254400 1324023555492 -349900046361984 46529871681675420 -14270444316475610112 3245904575339035225980", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(1728z-1)^2", "discr_factors": "2985984, (z-1/1728)^2", "dm_basis": ["-1/6-108*lambda", "-1/3", "3/2", "1", "-4/3", "4", "-1", "0", "-2", "-4", "0", "0", "4", "0", "0", "0"], "q": "0 1 -864 529632 -272074752 126845233200 -55579615921152 23323579295205888 -9484471534401552384 3765369834109277512344", "yuk": "1 -384 -11232 -4448256 6157546272 -408406800384 285989083527168 -120015715902160896 23823294307175361312 -10403153906710724219904", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","-4","1","0","0","0","1","1"]},{"re":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","-1/6","1","7/6"],"monodromy":["7/6+108*lambda","1/4-54*lambda","-1/18-36*lambda","-1/27*(-8*I*lambda*Pi^3)^(3/2)/Zeta(5)^(2/3)","4/3","1/3","-4/9","-1/18+36*lambda","2","3","1/3","1/4+54*lambda","-4","2","4/3","7/6-108*lambda"],"monodromy_dm":["0","1","-2","-1","1","-3","1","0","4","-16","5","0","-6","24","-6","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -79920*X^4-211680*X^3-197340*X^2-91500*X-17100, 47775744*X^4+374740992*X^3+652800384*X^2+431516160*X+104315760, 33538572288*X^4+38698352640*X^3-188170739712*X^2-249389383680*X-81864794880, -8916100448256*X^4-84702954258432*X^3-158229824274432*X^2-109841404133376*X-25973259337728, -185752092672*(12*X+7)*(12*X+11)*(12*X+13)*(12*X+17)]", "text": "This is operator \"5.64\" from ...", "degz": 5, "h3": null, "sol": "1 684 761004 985011120 1373164693740 2000308394975184 2999737945992631536 4592165354561372296896 7138856745753215194714860 11230855067389469877341467920", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 -17100 -91500 -197340 -211680 -79920 104315760 431516160 652800384 374740992 47775744 -81864794880 -249389383680 -188170739712 38698352640 33538572288 -25973259337728 -109841404133376 -158229824274432 -84702954258432 -8916100448256 -3160943360999424 -14016109904658432 -22415076526915584 -15407021574586368 -3851755393646592", "new_number": "5.64", "id": 276, "operator_tex": "5^{2} \\theta^4-2^{2} 3 5 x\\left(1332\\theta^4+3528\\theta^3+3289\\theta^2+1525\\theta+285\\right)+2^{4} 3^{2} x^{2}\\left(331776\\theta^4+2602368\\theta^3+4533336\\theta^2+2996640\\theta+724415\\right)+2^{8} 3^{5} x^{3}\\left(539136\\theta^4+622080\\theta^3-3024864\\theta^2-4008960\\theta-1315985\\right)-2^{15} 3^{8} x^{4}\\left(41472\\theta^4+393984\\theta^3+735984\\theta^2+510912\\theta+120811\\right)-2^{20} 3^{11} x^{5}(12\\theta+7)(12\\theta+11)(12\\theta+13)(12\\theta+17)", "superseek": "468/5 11885484", "discriminant": "5 25 -79920 47775744 33538572288 -8916100448256 -3851755393646592", "aesz": "272", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "467bb784f4bd6e978748e98f6ea4a573", "dim_h": null, "inst": " 468/5 -315477/5 11885484 -14354122356/5 808514230608 -1258871905551543/5 444331666288762812/5 -169531638476468437764/5 13514603472770718331560 -5523207855313637518334676", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+432z)(1728z+5)^2(1728z-1)^2", "discr_factors": "-3851755393646592, (z-1/1728)^2, -1/432+z, (z+5/1728)^2", "dm_basis": null, "q": "0 1 -924 669222 -445396592 285409255425 -178021670149224 108757332969381554 -65384540320368271296 38818215719959795717140", "yuk": "1 468/5 -2523348/5 1604540808/5 -918666354132/5 505321394130468/5 -271916329997116296/5 152405761537045644984/5 -17360039780174101297860 49260729658249269923077008/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/1728","im":"0","approx_re":"-0.00289351851852","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728","im":"0","approx_re":"0.000578703703704","approx_im":"0.0","exponents":["0","-1/6","1","7/6"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["7/12","11/12","13/12","17/12"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 744+3900*X+8364*X^2+8928*X^3+5328*X^4, 6786432+28100736*X+43811712*X^2+31933440*X^3+11653632*X^4, 12405104640+47235280896*X+63285940224*X^2+43643142144*X^3+15085191168*X^4, 3783743373312+20662340419584*X+39428461559808*X^2+38326848454656*X^3+14148117725184*X^4, -232644176510976+8284543333171200*X+27803373231144960*X^2+26641308139388928*X^3+9629388484116480*X^4, 1749267579144241152+8489268887597088768*X+15234976500336820224*X^2+11647708310387294208*X^3+4622106472375910400*X^4, 528029443404224004096+2475969995122327683072*X+4605836657593147195392*X^2+4153239991818098049024*X^3+1597399996853114634240*X^4, 30670079939579800977408*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"8.76\" from ...", "degz": 8, "h3": null, "sol": "1 -744 843624 -1099121280 1536242069160 -2240456761335744 3361795804206556416 -5148054252348430934016 8004598540092218178873000 -12594534180181314007557768000", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 744 3900 8364 8928 5328 6786432 28100736 43811712 31933440 11653632 12405104640 47235280896 63285940224 43643142144 15085191168 3783743373312 20662340419584 39428461559808 38326848454656 14148117725184 -232644176510976 8284543333171200 27803373231144960 26641308139388928 9629388484116480 1749267579144241152 8489268887597088768 15234976500336820224 11647708310387294208 4622106472375910400 528029443404224004096 2475969995122327683072 4605836657593147195392 4153239991818098049024 1597399996853114634240 245360639516638407819264 1042782717945713233231872 1625514236797729451802624 1104122877824872835186688 276030719456218208796672", "new_number": "8.76", "id": 525, "operator_tex": "\\theta^4+2^{2} 3 x\\left(444\\theta^4+744\\theta^3+697\\theta^2+325\\theta+62\\right)+2^{7} 3^{2} x^{2}\\left(10116\\theta^4+27720\\theta^3+38031\\theta^2+24393\\theta+5891\\right)+2^{12} 3^{4} x^{3}\\left(45468\\theta^4+131544\\theta^3+190749\\theta^2+142371\\theta+37390\\right)+2^{17} 3^{6} x^{4}\\left(148068\\theta^4+401112\\theta^3+412641\\theta^2+216243\\theta+39599\\right)+2^{23} 3^{9} x^{5}\\left(58320\\theta^4+161352\\theta^3+168390\\theta^2+50175\\theta-1409\\right)+2^{29} 3^{12} x^{6}\\left(16200\\theta^4+40824\\theta^3+53397\\theta^2+29754\\theta+6131\\right)+2^{35} 3^{17} x^{7}\\left(360\\theta^4+936\\theta^3+1038\\theta^2+558\\theta+119\\right)+2^{43} 3^{20} x^{8}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "-204 66054580/3", "discriminant": "8 1 5328 11653632 15085191168 14148117725184 9629388484116480 4622106472375910400 1597399996853114634240 276030719456218208796672", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a1b606169a188129e64002b152d24330", "dim_h": null, "inst": " -204 6654 66054580/3 6573546582 118182295200 -2656890725215682/3 -438640212197072580 -50520199191793858002 193901718038378149238992/3 45978267847610876532551280", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(432z+1)(864z+1)(1728z+1)^2(497664z^2+288z+1)^2", "discr_factors": "276030719456218208796672, z+1/432, (z^2+1/1728*z+1/497664)^2, (z+1/1728)^2, z+1/864", "dm_basis": null, "q": "0 1 924 641502 372437552 183579544365 76122109346184 26165909538619154 7481478465451494336 2059935154025021071110", "yuk": "1 -204 53028 594491016 420707034276 14772786899796 -191296131620984856 -150453592783595895144 -25866341985777748262748 47118117483325890859566072", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/864","im":"0","approx_re":"-0.00115740740741","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1728","im":"0","approx_re":"-0.000578703703704","approx_im":"0.0","exponents":["0","-1/6","1","7/6"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3456","im":"-1/3456*23^(1/2)","approx_re":"-0.000289351851852","approx_im":"-0.001388","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3456","im":"1/3456*23^(1/2)","approx_re":"-0.000289351851852","approx_im":"0.001388","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}]}